Mathematics

# Integrate the following function with respect to $x$$\dfrac{(\sin^{-1}{x})^{3/2}}{\sqrt{1-x^{2}}}$

##### SOLUTION
According to question,

Let,   $sin^{-1}x=t$

$\implies \dfrac{1}{\sqrt{1-x^2}}dx=dt$

Substituting these values, we get

$\implies \int t^{\frac{3}{2}}dt$

$\implies \dfrac{2t^{\frac{5}{2}}}{5}+C$

$\implies \dfrac{2(sin^{-1}x)^{\frac{5}{2}}}{5}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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